Rocky Balboa, the boxing legend, and his rival Ivan Drago decided to have a friendly competition to see who could throw the most punches in a given time period. They agreed to throw a combination of jabs and hooks, with jabs counting as 1 point and hooks counting as 2 points. Rocky can throw an average of 30 punches per minute, while Ivan can throw 25 punches per minute. They each have 3 minutes to throw punches. Rocky wants to throw the most punches and earn the most points in the competition. If x represents the number of jabs Rocky throws and y represent the number of hooks he throws, solve the number of jabs and hooks Rocky throws.

Answer 1

Let's set up the system of equations to solve for the number of jabs and hooks Rocky throws:

x + y = 30 (Rocky's punches per minute)
x = 30 - y

To earn the most points, we want to maximize the total points Rocky earns, which is given by:

1*x + 2*y = total points

Since we have 3 minutes to throw punches, Rocky wants to maximize the total points earned over the 3-minute period. We can express this as:

3*(1*x + 2*y) = 3*(total points)

Substitute x = 30 - y into the equation above:

3*(1*(30 - y) + 2*y) = 3*(total points)

Simplify:

90 - 3y + 6y = 3*(total points)
90 + 3y = 3*(total points)
30 + y = total points

Since Rocky wants to maximize the total points earned, he needs to maximize y, the number of hooks thrown. Since he can throw a maximum of 30 punches per minute, he will throw 30 - y jabs and y hooks in order to earn the maximum points possible.

Therefore, Rocky will throw 30 - y jabs and y hooks in the competition, where y = 10.

Answer 2

Rocky Balboa, the boxing legend, and his rival Ivan Drago decided to have a friendly competition to see who could throw the most punches in a given time period. They agreed to throw a combination of jabs and hooks, with jabs counting as 1 point and hooks counting as 2 points. Rocky can throw an average of 30 punches per minute, while Ivan can throw 25 punches per minute. They each have 3 minutes to throw punches. Rocky wants to throw the most punches and earn the most points in the competition. If x represents the number of jabs Rocky throws and y represent the number of hooks he throws, solve the number of jabs and hooks Rocky throws.

Answer 3

To maximize the number of points Rocky earns, we need to maximize the number of hooks (2 points each) he throws. Since Rocky can throw 30 punches per minute, let's maximize the number of hooks he throws in total.

Since hooks (y) are worth 2 points each, we want to maximize y.

Given:
- Total punches = 30 per minute
- Total hooks = y
- Total jabs = x = 30 - y

To calculate the total points Rocky can earn:
Total points = 2y + 1(30 - y)
Total points = 2y + 30 - y
Total points = y + 30

Since we have 3 minutes:
Total points in 3 minutes = 3(y + 30)

To maximize the number of points, we need to maximize y. Since y can't exceed the maximum number of punches Rocky can throw (30 per minute), let's set y = 30.

So, Rocky should throw 30 hooks and 0 jabs in order to maximize the number of points and punches thrown.